>> In computer chess, the methods that defeated the world champion, Kasparov, in 1997, were based on massive, deep search. "Massive, deep search" that started from a book of opening moves and the combined expert knowledge of several chess Grandmasters. And that was an instance of the minimax algorithm with alpha-beta cutoff, i.e. a search algorithm specifically designed for two-player, deterministic games like chess.…
My guess is that we're doing pattern recognision, where we recognize taht a current game state is similar to a situation that we've been in before (in some previous game), and recall the strategy we took and the outcomes it had lead to. With large enough body of experience, you can to remember lots of past attempted strategies for every kind of game state (of course, within some similarity distance).